Endomorphism/Basis/To scalar multiples/Dimension/Exercise

Let $V$ be a $K$-vector space, and let $v_1,\dots ,v_n$ denote a basis of $V$. Determine the dimension of the space of all endomorphisms

$\phi :V⟶V$

satisfying

$\phi (v_i)\in K{v}_i$

for all $i$. How do the matrices of such a $\phi$ with respect to this basis look like?

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